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Accession Number
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ADA564072
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Title
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Band-Gap Optimization for Wave Propagation in Periodic Media using Semi- Definite Programming.
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Publication Date
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Apr 2011
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Media Count
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8p
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Personal Author
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H. Men J. Peraire N. C. Nguyen P. A. Parrilo R. M. Freund
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Abstract
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Our research has focused on the optimal design of photonic crystals with large band-gaps, thereby enabling a wide variety of prescribed interaction with and control of mechanical and electromagnetic waves. We have developed computational methods to design two-dimensional photonic crystals with large absolute and relative band gaps. Our modeling methodology yields a series of finite-dimensional eigenvalue optimization problems that are large-scale and non-convex, with low regularity and non-differentiable objective. By restricting to appropriate eigen-subspaces, we have reduced the problem to a sequence of small-scale convex semidefinite programs (SDPs) for which modern SDP solvers can be efficiently applied. Among several illustrations we show that it is possible to design photonic crystals which exhibit multiple band gaps for the combined transverse electric and magnetic modes. The optimized crystals show complicated patterns which are far different from existing photonic crystal designs. We employ subspace approximation and mesh adaptivity to enhance computational efficiency.
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Keywords
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Band gap optimization
Band gaps
Computation science
Conic optimization
Eigenvalues
Optimization
Periodic media
Photonic band gap materials
Photonic crystal design
Photonic crystals
Semidefinite programming
Subspace methods
Wave propagation
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Source Agency
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Non Paid ADAS
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NTIS Subject Category
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49E - Optoelectronic Devices & Systems
46D - Solid State Physics
46C - Optics & Lasers
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Corporate Author
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Massachusetts Inst. of Tech., Cambridge.
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Document Type
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Technical report
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Title Note
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Final rept. 1 Jun 2008-31 May 2011.
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NTIS Issue Number
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1302
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Contract Number
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FA9550-08-1-0350
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